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Some Tests of Covariance Matrices for High Dimensional Multivariate Data
Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0001-9896-4438
Department of Energy and Technology, Swedish Univerity of Agricultural Sciences, SE-750 07 Uppsala, Sweden.
2011 (engelsk)Rapport (Annet vitenskapelig)
Abstract [en]

Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.

sted, utgiver, år, opplag, sider
Linköping, 2011. , s. 28
Serie
LiTH-MAT-R, ISSN 0348-2960 ; 2011:13
Emneord [en]
covariance testing; high dimensional data; sphericity
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-70062Lokal ID: LiTH-MAT-R--2011/13--SEOAI: oai:DiVA.org:liu-70062DiVA, id: diva2:435111
Tilgjengelig fra: 2011-08-17 Laget: 2011-08-17 Sist oppdatert: 2014-09-29

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